Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-26T08:49:42.125Z Has data issue: false hasContentIssue false

Coupled Quantum–Atomistic and Quantum–Continuum Mechanics Methods in Materials Research

Published online by Cambridge University Press:  31 January 2011

Get access

Abstract

The interface of quantum mechanics methods with classical atomistic simulation techniques, such as molecular dynamics and Monte Carlo, continues to be an area of considerable promise and interest. Such coupled quantum–atomistic approaches have been developed and employed, for example, to gain a comprehensive understanding of the energetics, kinetics, and dynamics of chemical processes involving surfaces and interfaces of hard materials. More recently, it has become possible to directly couple first-principles electronic structure techniques to continuum solid mechanics, either on the fly with feedback between length scales or by information passing between length scales. We discuss, with tutorial examples, the merging of quantum mechanics with molecular dynamics and Monte Carlo simulations, as well as quantum–continuum coupled techniques. We illustrate the opportunities offered by incorporation of information from quantum mechanics (reducing assumptions in higher length-scale models) and outline the challenges associated with achieving full predictive capability for the behavior of materials.

Type
Research Article
Copyright
Copyright © Materials Research Society 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Hohenberg, P., Kohn, W., Phys. Rev. 136, B864 (1964).CrossRefGoogle Scholar
2.Kohn, W., Sham, L.J., Phys. Rev. 140, A1133 (1965).CrossRefGoogle Scholar
3.Hughes, T.J.R., The Finite Element Method (Prentice-Hall, Englewood Cliffs, N.J., 1987).Google Scholar
4.Needleman, A., Acta Mater. 48, 105 (2000).CrossRefGoogle Scholar
5.Kubin, L.P., Canova, G., Scr. Metall. Mater. 27, 957 (1992).CrossRefGoogle Scholar
6.Zbib, H.M., de la Rubia, T. Diaz, Bulatov, V.V., Int. J. Mech. Sci. 124, 78 (2002).Google Scholar
7.Lu, G., Kaxiras, E., in Handbook of Theoretical and Computational Nanoscience, Rieth, M., Schommers, W., Eds., vol. X, chap. 22 (American Scientific, 2005).Google Scholar
8.Robertson, I.M., Lassila, D.H., Devincre, B., Phillips, R., Eds., Multiscale Phenomena in Materials—Experiments and Modeling (Mater. Res. Soc. Proc. 578 Materials Research Society, Warrendale, PA, 2000).Google Scholar
9.Kubin, L.P., Selinger, R.L., Bassani, J.L., Cho, K., Eds., Multiscale Modeling of Materials—2000 (Mater. Res. Soc. Proc. 653, Materials Research Society, Warrendale, PA, 2001).Google Scholar
10.Xu, X.-P., Needleman, A., J. Mech. Phys. Solids 42, 1397 (1994).CrossRefGoogle Scholar
11.Camacho, G.T., Ortiz, M., Int. J. Solids Struct. 33, 2899 (1996).CrossRefGoogle Scholar
12.Falk, M.L., Needleman, A., Rice, J.R., J. Phys. IV 11, 43 (2001).Google Scholar
13.Hirth, J.P., Lothe, J., Theory of Dislocations (Wiley, New York, 1982).Google Scholar
14.Cai, W., Arsenalis, A., Weinberger, C.R., Bulatov, V.V., J. Mech. Phys. Solids 54, 561 (2006).CrossRefGoogle Scholar
15.Tadmor, E.B., Waghmare, U.V., Smith, G.S., Kaxiras, E., Acta Mater. 50, 2989 (2002).CrossRefGoogle Scholar
16.Serebrinsky, S., Carter, E.A., Ortiz, M., J. Mech. Phys. Solids 54, 2403 (2004).CrossRefGoogle Scholar
17.Jiang, D.E., Carter, E.A., Acta Mater. 52, 4801 (2004).CrossRefGoogle Scholar
18.van der Wen, A., Ceder, G., Phys. Rev. B 67, 060101 (2003).CrossRefGoogle Scholar
19.Nguyen, O., Ortiz, M., J. Mech. Phys. Solids 50, 1727 (2002).CrossRefGoogle Scholar
20.Hayes, R.L., Ortiz, M., Carter, E.A., Phys. Rev. B 69, 172104 (2004).CrossRefGoogle Scholar
21.Ortiz, M., Phillips, R., Adv. Appl. Mech. 36, 1 (1999).Google Scholar
22.Abraham, F., Broughton, J., Bernstein, N., Kaxiras, E., Comput. Phys. 12, 538 (1998).CrossRefGoogle Scholar
23.Broughton, J., Abraham, F., Bernstein, N., Kaxiras, E., Phys. Rev. B 60, 2391 (1999).CrossRefGoogle Scholar
24.Lu, G., Tadmor, E.B., Kaxiras, E., Phys. Rev. B 73, 024108 (2006).CrossRefGoogle Scholar
25.Nix, W.D., Metall. Trans. A 20A, 2217 (1989).CrossRefGoogle Scholar
26.Sutton, A.P., Pethica, J.B., J. Phys. Condens. Matter 2, 5317 (1990).CrossRefGoogle Scholar
27.Fago, M., Hayes, R.L., Carter, E.A., Ortiz, M., Phys. Rev. B 70, 100102 (2004).CrossRefGoogle Scholar
28.Hayes, R.L., Fago, M., Ortiz, M., Carter, E.A., Multiscale Model. Simul. 4, 359 (2005).CrossRefGoogle Scholar
29.Hayes, R.L., Ho, G., Ortiz, M., Carter, E.A., Philos. Mag. 86, 2343 (2006).CrossRefGoogle Scholar
30.Watson, S., Carter, E.A., Comput. Phys. Commun. 128, 67 (2000).CrossRefGoogle Scholar
31.Zhou, B., Wang, Y., Carter, E.A., Phys. Rev. B 69, 155329 (2004).Google Scholar
32.Watson, S., Wesson, B.J., Carter, E.A., Madden, P.A., Europhys. Lett. 41, 37 (1998).CrossRefGoogle Scholar
33.Wang, Y.A., Carter, E.A., in Theoretical Methods in Condensed Phase Chemistry, in the series Progress in Theoretical Chemistry and Physics, Schwartz, S., Ed. (Kluwer, Dordrecht, 2000), pp. 117184.Google Scholar
34.Woodward, C., Rao, S.I., Phys. Rev. Lett. 88, 216402 (2002).CrossRefGoogle Scholar
35.Woodward, C., Mater. Sci. Eng. A 400, 59 (2005).CrossRefGoogle Scholar
36.Trinkle, D.R., Woodward, C., Science 310, 1665 (2005).CrossRefGoogle Scholar
37.Car, R., Parrinello, M., Phys. Rev. Lett. 55, 2471 (1985).CrossRefGoogle Scholar
38.Born, M., Oppenheimer, J.R., Annu. Phys. 84, 457 (1927).CrossRefGoogle Scholar
39.Barnett, R.N., Landman, U., Nitzan, A., Rajagopal, G., J. Chem. Phys. 94, 608 (1991).CrossRefGoogle Scholar
40.Gibson, D.A., Ionova, I.V., Carter, E.A., Chem. Phys. Lett. 240, 261 (1995).CrossRefGoogle Scholar
41.Marx, D., Hutter, J., in Modern Methods and Algorithms of Quantum Chemistry, Grotendorst, J., Ed. (John von Neumann Institute for Computing, Jülich, 2000), pp. 329477.Google Scholar
42.Radeke, M.R., Carter, E.A., Annu. Rev. Phys. Chem. 48, 243 (1997).CrossRefGoogle Scholar
43.Tse, J.S., Annu. Rev. Phys. Chem. 53, 249 (2002).CrossRefGoogle Scholar
44.Weakliem, P.C., Wu, C.J., Carter, E.A., Phys. Rev. Lett. 69, 200 (1992).CrossRefGoogle Scholar
45.Weakliem, P.C., Carter, E.A., J. Chem. Phys. 98, 737 (1993).CrossRefGoogle Scholar
46.Madden, P.A., Heaton, R., Aguado, A., Jahn, S., J. Mol. Struct.: THEOCHEM 771, 9 (2006).CrossRefGoogle Scholar
47.van Duin, A.C.T., Dasgupta, S., Lorant, F., Goddard, W.A., J. Phys. Chem. A 105, 9396 (2001).CrossRefGoogle Scholar
48.van Duin, A.C.T., Strachan, A., Stewman, S., Zhang, Q., Xu, X., Goddard, W.A., J. Phys. Chem A 107, 3803 (2003).CrossRefGoogle Scholar
49.Buehler, M.J., van Duin, A.C.T., Goddard, W.A., Phys. Rev. Lett. 96, 095505 (2006).CrossRefGoogle Scholar
50.Csányi, G., Albaret, T., Payne, M.C., De Vita, A., Phys. Rev. Lett. 93, 175503 (2004).CrossRefGoogle Scholar
51.Csányi, G., Moras, G., Kermonde, J.R., Payne, M.C., in Top. Appl. Phys. 104, Drabold, D.A., Estreicher, S.K., Eds. (Springer, Berlin, 2007), pp. 193212.Google Scholar
52.Govind, N., Wang, Y.A., Carter, E.A., J. Chem. Phys. 110, 7677 (1999).CrossRefGoogle Scholar
53.Bortz, A.B., Kalos, M.H., Lebowitz, J.L., J. Comp. Phys. 17, 10 (1975).CrossRefGoogle Scholar
54.Fichthorn, K.A., Weinberg, W.H., J. Chem. Phys. 95, 1090 (1991).CrossRefGoogle Scholar
55.Reuter, K., Scheffler, M., Phys. Rev. B 73, 045433 (2006).CrossRefGoogle Scholar
56.Reuter, K., Stampfl, C., Scheffler, M., in Handbook of Materials Modeling, Part A: Methods, Yip, S., Ed. (Springer, Berlin Heidelberg, 2005), pp. 149194.CrossRefGoogle Scholar
57.Radeke, M.R., Carter, E.A., Phys. Rev. B 54, 11803 (1996).CrossRefGoogle Scholar
58.Voter, A.F., Montalenti, F., Germann, T.C., Annu. Rev. Mater. Res. 32, 321 (2002).CrossRefGoogle Scholar
59.Feibelman, P.J., Phys. Rev. Lett. 65, 729 (1990).CrossRefGoogle Scholar
60.Henkelman, G., Jónsson, H., Phys. Rev. Lett. 90, 116101 (2003).CrossRefGoogle Scholar
61.Henkelman, G., Jónsson, H., J. Chem. Phys. 121, 9776 (2004).Google Scholar
62.Karim, A., Al-Rawi, A.N., Kara, A., Rahman, T.S., Trushin, O., Ala-Nissila, T., Phys. Rev. B 73, 165411 (2006).CrossRefGoogle Scholar
63.Cui, Q., Guo, H., Karplus, M., J. Chem. Phys. 117, 5617 (2002).CrossRefGoogle Scholar
64.Gao, J., Truhlar, D.G., Annu. Rev. Phys. Chem. 53, 467 (2002).CrossRefGoogle Scholar
65.Lin, H., Truhlar, D., Theo. Chem. Acc. 117, 185 (2007).CrossRefGoogle Scholar